Wave localization in one-dimensional periodic-on-average disordered system composed of single-negative metamaterials

By using the transfer-matrix method, we study the Anderson localization behavior in one-dimensional periodic-onaverage disordered system composed of two different single-negative(SNG) metamaterials. Non-dispersive and dipersive models have been studied respectively. It was found that the disorder has great effect on waves with frequency in the pass band of the corresponding periodic structure. However,inside the gap, the effect can be almost ignored. These features are different from those we ever found in the random single-negative system. The main reason of the difference should be the number of the interfaces between two kinds of single negative metamateirals, which should be the basic mechanism of the wave propagation in systems made of single negative metamaterials. In periodic-on-average disordered systems,the number of the interface is the same as that in periodic one. However, there is an obvious decrease in random systems, which will have a great effect on the ability of wave transport, leading to small localization length. In the case of a dispersive model, it has been proved that the randomness has no effect on the wave propagation with frequency at the center of the gap. Especially,this special point becomes a delocalization point when the ratio of effective optical thickness of two single negative materials equals one. The results facilitates further understanding of the wave transport mechanism in systems composed of metamaterials.